The formalism for DFTB with self-consistent charges (SCC) has been discussed in detail elsewhere[1]}, [2]}, [3]}, [4]}, [5]}. Briefly, the method assumes neutral, spherically symmetric, atom-centered charge densities \(n_0\)  and that the true charge density of the system is within a small perturbation, i.e., \(n(\mathrm {r}) = n_0(\mathrm {r}) + \delta n\) . In its most typical form, a second-order Taylor expansion of the Kohn-Sham total energy in \(\delta n\)  is employed to yield the following energy expression:
\(\begin{split}E[\delta n] \approx & \sum _a f_a \left<\psi _a \left| \hat{T} + \hat{V}\left[n_0\right] \right| \psi _a \right> \\& +\frac{1}{2} \int \int ^{^{\prime }} \left(\frac{\delta ^2E_{xc}[n_0]}{\delta n \delta n^{^{\prime }}} + \frac{1}{\left| \mathbf {r} - \mathbf {r^{^{\prime }}}\right|}\right)\delta n \delta n^{^{\prime }} \\& -\frac{1}{2} \int \frac{n^{^{\prime }}_0 n_0}{\left| \mathbf {r} - \mathbf {r^{^{\prime }}} \right|} + E_{xc}[n_0] - \int V_{xc}[n_0]n_0 + E_{II}, \\\end{split}\) 
